MinT - Best Known (94, 139, s)-Nets in Base 8

Best Known (94, 139, s)-Nets in Base 8

(94, 139, 402)-Net over F₈ — Constructive and digital

Digital (94, 139, 402)-net over F₈, using

1 times m-reduction [i] based on digital (94, 140, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 34, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]
  2. digital (60, 106, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 53, 177)-net over F₆₄, using
      - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(94, 139, 576)-Net in Base 8 — Constructive

(94, 139, 576)-net in base 8, using

9 times m-reduction [i] based on (94, 148, 576)-net in base 8, using
- trace code for nets [i] based on (20, 74, 288)-net in base 64, using
  - 3 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(94, 139, 1779)-Net over F₈ — Digital

Digital (94, 139, 1779)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 139, 597836)-Net in Base 8 — Upper bound on s

There is no (94, 139, 597837)-net in base 8, because

1 times m-reduction [i] would yield (94, 138, 597837)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42308 701723 009718 705307 727574 076302 951126 759910 648722 485825 843292 841942 912468 943198 025012 303841 479998 943241 672589 491824 734544 > 8¹³⁸ [i]